Only with foot on brake, is it a miss fire or drop in rev as it may try and creep forward but can't as the brake is on so the revs fluctuate? Not an auto driver so only a question.
Whooshing would probably be pressured side of the turbo. Only takes a small hole. There is a weak point somewhere that I've seen mentioned on here, a elbow joint that might even be plastic
While a joint is ok, I'm not sure a reputable garage would use one. By the time the joint was made a complete pipe could be installed. A pain on axle stands to get in but probably easier on a ramp.
Depending on level of security a money tin might be ok.
Leaving out of sight isn't always best as anyone who has access to the car,eg mechanics, may find it and you possibly wouldnt know straight away.